1)

The volume of the tetrahedron included between the plane 3x+4y-5z-60=0  and the coordinate planes is 


A) 60

B) 600

C) 720

D) 400

Answer:

Option B

Explanation:

The given equation of the plane is $3x+4y-5z-60=0$ it can be written in the form $\frac{x}{20}+\frac{y}{15}+\frac{z}{-12}=1$

 which meets the coordinate axes at the pints A(20,0,0), B(0,15,0) and C(0,0,-12) .The coordinates of the origin are O(0,0,0) Therefore , volume of the tetrahedron  OABC is = 

$\frac{1}{6}\begin{bmatrix}20 &0&0 \\0 & 15&0\\0&0&-12 \end{bmatrix}=\frac{1}{6}|20\times15\times(-12)|=600$